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Question

Physics Question on Gravitation

A satellite is orbiting just above the surface of the earth with period T. If d is the dependent of the earth and G is the universal constant of gravitation, the quantity 3π/Gd respectively:

A

T2

B

T3

C

T\sqrt{T}

D

T

Answer

T2

Explanation

Solution

The correct option is (A): T2

T=2πGMr32T=\frac{2\pi}{\sqrt{GM}}r^{\frac{3}{2}}

⇒T2=4π2R3G(43πR3d)(r=R)\Rightarrow T^2=\frac{4\pi^2R^3}{G(\frac{4}{3}\pi R^3d)}(r=R)

T2=3πGdT^2=\frac{3\pi}{Gd}